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analytic functions apolar Apply Th arbitrary assume bounded circle C2 circular region closed interior coefficients complex numbers conjugate imaginary convex hull convex region corresponding critical points curve defined disk due to Marden ellipse equation exterior finite fk(z given half-plane Hence Hint homogeneous polynomial ineq inequality infrapolynomial inverse distance law Jensen circles Kakeya Laguerre's Theorem least one zero Lemma Let us denote lies linear locus logarithmic derivative Math mathematical induction matrix modulus Nagy nomial non-real zero nth degree polynomial number of zeros off(z polynomial f(z polynomial of degree positive number proof of Th prove Th Prove the following radius rational function real polynomial real zeros result due Rolle's Theorem satisfy sector star-shaped region Stieltjes polynomial symmetric Theorem Th unit circle upper half-plane zeros of F(z zeros of polynomials
Page 235 - A sufficient condition for the maximum number of imaginary roots of an equation of the nth degree, Ann.
Page 238 - Theorem of Grace on the zeros of polynomials, revisited, Proc. Amer, Math. Soc. 15 (1964), 354-360.